General Events - Department of Mathematics

Title: The Motion of Waves: From Phase Recover Problems to the Dynamics of Fluids and Plasmas

Abstract: Reconstructing signals from amplitude-only measurements is a central problem in X-ray crystallography, speech recognition, and quantum mechanics. In imaging applications, the high oscillation of scattering waves makes it impossible for detectors to directly record phase information. For this reason, recovery from phaseless measurements has been central to many fundamental physical discoveries, including the double helix structure of DNA. Similarly, in quantum mechanics, phase information cannot be directly accessed through experiments, as only positive quantities such as the probability densities associated to the wave function ψ can be measured. In the first part of this talk, we will discuss recent developments related to classifying instabilities in phase retrieval and constructing non-trivial examples where phase can be stably recovered. In the second part of the talk, we will discuss the underlying PDEs governing wave motion, including the Schrodinger equation, the equations of magnetohydrodynamics, and the fundamental models of fluid and plasma dynamics.